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A uniformly charged solid shpere fo rad...

A uniformly charged solid shpere fo radius `R` has potential `V_(0)` (measured with respect to `oo`) on its surface. For this sphere the equipotentail surfaces with potentials `(3V_(0))/(2) , (5 V_(0))/(4), (3V_(0))/(4)` and `(V_(0))/(4)` have radius `R_(1), R_(2), R_(3)` and `R_(4)` respecatively. Then

A

(a) `R_1=0` and `R_2lt(R_4-R_3)`

B

(b) `2RltR_4`

C

(c) `R_1=0` and `R_2gt(R_4-R_3)`

D

(d) `R_1!=0` and `(R_2-R_1)gt(R_4-R_3)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
We know, `V_0=(Kq)/(R)=` Vsurface
Now, `V_i=(Kq)/(2R^3)(3R^2-r^2)` [For rltR]
At the centre of sphare `r=0`. Hence
`V=3/2V_0`
Now, `5/4(Kq)/(R)=(Kq)/(2R^3)(3R^2-r^2)`
`R_2=R/sqrt2`
`3/4(Kq)/(R)=(Kq)/(R^3)`
`1/4(Kq)/(R)=(Kq)/(R_4)`
`R_4=4R`
Also, `R_1=0` and `R_2lt(R_4-R_3)`
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